First off, if you don't know what contrapuntal music in film is (correct me if I'm not explaining correctly): Music opposite to the emotion expected from the narrative. So for example, to put it plainly, fun music over a sad scene.

I just watched "9" and I loved the sound. Specifically, I loved one scene where they used contrapuntal music. The song was (somewhere) Over The Rainbow, which was [stop reading here if you haven't watched it] used diagetically when they where celebrating their victory and everything is hunky-dory but then they get attacked again but the beautiful music keeps playing over part of the attack. I thought it was a very well crafted scene.

"Over The Rainbow":

Trailer for "9":

At film school, I went through a contrapuntal phase, but I haven't had the opportunity to use it since. So my question is:

Have you used this technique for your films (any thoughts on it)? And what are your favorite films that use it?

Yes the music in fallout 3 is great & really important to the feel of the game. Another good example from a recent game is in Aliens Vs Predator. When you play as a marine you get locked in a deserted nightclub, aliens chew through the power cables which sets off dance music and strobe lighting while they attack you!
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Haydn PayneMay 25 '10 at 6:29

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I can't find any good clips on youtube but Bioshock has the same optimistic 50's style music, set in an extremely scary and disturbing underwater city. Great game, amazing atmosphere, largely due to the sound.
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MechMay 25 '10 at 11:29

I love the official Bioshock 2 trailer for that!
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ragamesoundJun 7 '10 at 16:19

When I first saw the question I thought you meant "music that follows the rules of counterpoint" since that's what contrapuntal means in music theory. But to answer the question, the first time I noticed this effect was at the end of Dr. Strangelove. As nuclear bombs destroy the world, the sappy sentimental song "We'll Meet Again" plays in the background. It's quite ironic and effective. It's used similarly in the video game Fallout 3 (as mentioned already), where the radio plays cheery oldies that lie in stark contrast to the nuclear wasteland before the player.

I've also seen some mediocre films where it happened unintentionally, to comical effect.

I used a version of "What a Wonderful World" sung by Sarah Brightman for a WWII movie trailer. The scenes were mostly gun shots, explosions, and general mayhem. So, the song was in stark contrast to the visuals.

My favourite film music is from Alfred Hitchcock's 'The Birds', when the school children are singing and you see crows slowly gathering on a climbing frame in the background.

The images you see make you feel pretty tense but the music is completely childlike & carefree. The children's voices are source music (i.e. within the diegesis) which I think increases the tension because they are unaware of the danger.

Its a children's roundelay song, and every time they reach the end of a verse and start the next one it sends shivers down my spine!

I can't say it's my best loved examples but at least the ones that come to mind.

The first one is the opening fight scene in Watchmen with Bob Dylan's song playing. Great scene I find :)

The second one may be slightly less impressive, probably because the video is made with a video game engine. I am thinking about the Gears of War trailer, made by Digital Domain, using the song Mad World.

The example that comes to my mind is the scene from the bollywood movie Mera Naam Joker {my name is joker} where the prtagonist receives the news of his mother's death while the audience claps and cheers in the background.:)

My favorite is from Batman (1989) while the Joker is killing his boss, there is a kind of circus vibe to the music. While fitting to the scene from the Joker's point of view, it is not what the audience would expect.